The main purpose of algebra is to solve problems.

Using equations to solve problems can be useful when we are given a word problem.

Example

I think of a number and multiply it by 6.  After adding 20 to the result, my answer is 2.  What is the number I first thought of?

 Let the number I first thought of be x

When I multiply by 6 and add 20, this becomes 6x + 20.  This is equal to 2.

The equation is:  6x + 20 = 2

Solve to get:

6x = -18

 x = -3

The number I first thought of is -3

We can check our answer by putting it back into the equation: 

 -3 × 6 = -18

 -18 + 20 = 2 so it works.

Let's have a go at some questions now.